Multiply the following complex numbers: $({-4+5i}) \cdot ({5-5i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4+5i}) \cdot ({5-5i}) = $ $ ({-4} \cdot {5}) + ({-4} \cdot {-5}i) + ({5}i \cdot {5}) + ({5}i \cdot {-5}i) $ Then simplify the terms: $ (-20) + (20i) + (25i) + (-25 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (20 + 25)i - 25i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (20 + 25)i - (-25) $ The result is simplified: $ (-20 + 25) + (45i) = 5+45i $